Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-y &= -4 \\ -x+2y &= 8\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $2y = x+8$ Divide both sides by $2$ to isolate $y$ $y = {\dfrac{1}{2}x + 4}$ Substitute this expression for $y$ in the first equation. $-2x-({\dfrac{1}{2}x + 4}) = -4$ $-2x - \dfrac{1}{2}x - 4 = -4$ Simplify by combining terms, then solve for $x$ $-\dfrac{5}{2}x - 4 = -4$ $-\dfrac{5}{2}x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $-2( 0)-y = -4$ $-y = -4$ $-y = -4$ $y = 4$ The solution is $\enspace x = 0, \enspace y = 4$.